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

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

(32, 98, 120)-Net over F₃₂ — Constructive and digital

Digital (32, 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]

(32, 98, 192)-Net in Base 32 — Constructive

(32, 98, 192)-net in base 32, using

t-expansion [i] based on (31, 98, 192)-net in base 32, using
- base change [i] based on digital (3, 70, 192)-net over F₁₂₈, using
  - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
      - a function field by SÃ©mirat [i]

(32, 98, 273)-Net over F₃₂ — Digital

Digital (32, 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]

(32, 98, 12509)-Net in Base 32 — Upper bound on s

There is no (32, 98, 12510)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3200 897967 027780 082011 658065 751248 314761 837978 544814 366991 619537 601827 405619 886824 044920 685982 147145 697347 217793 132016 962747 827622 916922 750699 769546 > 32⁹⁸ [i]