MinT - Best Known (100, 246, s)-Nets in Base 4

Best Known (100, 246, s)-Nets in Base 4

(100, 246, 104)-Net over F₄ — Constructive and digital

Digital (100, 246, 104)-net over F₄, using

t-expansion [i] based on digital (73, 246, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(100, 246, 144)-Net over F₄ — Digital

Digital (100, 246, 144)-net over F₄, using

t-expansion [i] based on digital (91, 246, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(100, 246, 938)-Net in Base 4 — Upper bound on s

There is no (100, 246, 939)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13048 536711 469174 865701 969189 691041 658933 591219 012169 079823 474442 590468 164690 297483 305461 522936 489025 960092 229909 630163 421545 453736 008043 358905 412076 > 4²⁴⁶ [i]