MinT - Best Known (93, 93+141, s)-Nets in Base 4

Best Known (93, 93+141, s)-Nets in Base 4

(93, 93+141, 104)-Net over F₄ — Constructive and digital

Digital (93, 234, 104)-net over F₄, using

t-expansion [i] based on digital (73, 234, 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]

(93, 93+141, 144)-Net over F₄ — Digital

Digital (93, 234, 144)-net over F₄, using

t-expansion [i] based on digital (91, 234, 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]

(93, 93+141, 848)-Net in Base 4 — Upper bound on s

There is no (93, 234, 849)-net in base 4, because

1 times m-reduction [i] would yield (93, 233, 849)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 200 095576 158641 589810 502817 125605 285060 626523 090712 425207 871603 566204 271943 254644 442144 352751 161897 411718 928229 463340 954033 715388 407059 305160 > 4²³³ [i]