MinT - Best Known (238−140, 238, s)-Nets in Base 4

Best Known (238−140, 238, s)-Nets in Base 4

(238−140, 238, 104)-Net over F₄ — Constructive and digital

Digital (98, 238, 104)-net over F₄, using

t-expansion [i] based on digital (73, 238, 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]

(238−140, 238, 144)-Net over F₄ — Digital

Digital (98, 238, 144)-net over F₄, using

t-expansion [i] based on digital (91, 238, 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]

(238−140, 238, 942)-Net in Base 4 — Upper bound on s

There is no (98, 238, 943)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 203110 120913 996736 788840 907064 375111 263944 299596 622482 744621 811027 970986 184060 733054 892711 185109 644700 360712 903783 572285 584140 872200 349314 311722 > 4²³⁸ [i]