MinT - Best Known (98−49, 98, s)-Nets in Base 32

Best Known (98−49, 98, s)-Nets in Base 32

(98−49, 98, 240)-Net over F₃₂ — Constructive and digital

Digital (49, 98, 240)-net over F₃₂, using

5 times m-reduction [i] based on digital (49, 103, 240)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (11, 38, 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]
  2. digital (11, 65, 120)-net over F₃₂, using
    - net from sequence [i] based on digital (11, 119)-sequence over F₃₂ (see above)

(98−49, 98, 513)-Net in Base 32 — Constructive

(49, 98, 513)-net in base 32, using

t-expansion [i] based on (46, 98, 513)-net in base 32, using
- 10 times m-reduction [i] based on (46, 108, 513)-net in base 32, using
  - base change [i] based on digital (28, 90, 513)-net over F₆₄, using
    - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
        the Hermitian function field over F₆₄ [i]

(98−49, 98, 736)-Net over F₃₂ — Digital

Digital (49, 98, 736)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(98−49, 98, 383090)-Net in Base 32 — Upper bound on s

There is no (49, 98, 383091)-net in base 32, because

1 times m-reduction [i] would yield (49, 97, 383091)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 99 897750 358099 644840 068246 392615 480068 233963 652228 131739 402928 883599 412422 012194 622304 534838 489139 219177 057005 944718 027020 836751 838067 861075 414132 > 32⁹⁷ [i]