MinT - Best Known (98−62, 98, s)-Nets in Base 32

Best Known (98−62, 98, s)-Nets in Base 32

(98−62, 98, 120)-Net over F₃₂ — Constructive and digital

Digital (36, 98, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 98, 120)-net over F₃₂, using
- net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
    - a function field by SÃ©mirat [i]

(98−62, 98, 216)-Net in Base 32 — Constructive

(36, 98, 216)-net in base 32, using

10 times m-reduction [i] based on (36, 108, 216)-net in base 32, using
- base change [i] based on (18, 90, 216)-net in base 64, using
  - 1 times m-reduction [i] based on (18, 91, 216)-net in base 64, using
    - base change [i] based on digital (5, 78, 216)-net over F₁₂₈, using
      - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
        a function field by SÃ©mirat [i]

(98−62, 98, 273)-Net over F₃₂ — Digital

Digital (36, 98, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 98, 273)-net over F₃₂, using
- net from sequence [i] based on digital (30, 272)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 30 and N(F) ≥ 273, using
    - a curve from the manYPoints database [i]

(98−62, 98, 315)-Net in Base 32

(36, 98, 315)-net in base 32, using

4 times m-reduction [i] based on (36, 102, 315)-net in base 32, using
- base change [i] based on digital (19, 85, 315)-net over F₆₄, using
  - net from sequence [i] based on digital (19, 314)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 19 and N(F) ≥ 315, using
      - a curve from the manYPoints database [i]

(98−62, 98, 22939)-Net in Base 32 — Upper bound on s

There is no (36, 98, 22940)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3198 689031 437605 008791 843199 079683 556798 935555 454545 319439 992718 396746 864647 461179 930455 776536 846819 932968 681066 586291 271909 198322 223720 453201 884256 > 32⁹⁸ [i]