MinT - Best Known (110−77, 110, s)-Nets in Base 32

Best Known (110−77, 110, s)-Nets in Base 32

(110−77, 110, 120)-Net over F₃₂ — Constructive and digital

Digital (33, 110, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 110, 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]

(110−77, 110, 177)-Net in Base 32 — Constructive

(33, 110, 177)-net in base 32, using

32² times duplication [i] based on (31, 108, 177)-net in base 32, using
- t-expansion [i] based on (25, 108, 177)-net in base 32, using
  - base change [i] based on digital (7, 90, 177)-net over F₆₄, using
    - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
        a function field by GarcÃa and Quoos [i]

(110−77, 110, 273)-Net over F₃₂ — Digital

Digital (33, 110, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 110, 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]

(110−77, 110, 10046)-Net in Base 32 — Upper bound on s

There is no (33, 110, 10047)-net in base 32, because

1 times m-reduction [i] would yield (33, 109, 10047)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 115 601482 334863 542009 316540 542747 730554 855040 948494 713393 806906 833053 055450 970240 158121 038691 021072 777942 291830 977015 196132 598204 211224 705683 645197 266414 768269 659245 > 32¹⁰⁹ [i]