MinT - Best Known (93, 93+149, s)-Nets in Base 4

Best Known (93, 93+149, s)-Nets in Base 4

(93, 93+149, 104)-Net over F₄ — Constructive and digital

Digital (93, 242, 104)-net over F₄, using

t-expansion [i] based on digital (73, 242, 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+149, 144)-Net over F₄ — Digital

Digital (93, 242, 144)-net over F₄, using

t-expansion [i] based on digital (91, 242, 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+149, 804)-Net in Base 4 — Upper bound on s

There is no (93, 242, 805)-net in base 4, because

1 times m-reduction [i] would yield (93, 241, 805)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 906277 983579 396017 787090 298274 564064 887818 348150 528614 882837 666677 722014 956245 458746 171043 999649 834116 366922 615576 186252 586704 172857 191934 292128 > 4²⁴¹ [i]