MinT - Best Known (96, 96+163, s)-Nets in Base 4

Best Known (96, 96+163, s)-Nets in Base 4

(96, 96+163, 104)-Net over F₄ — Constructive and digital

Digital (96, 259, 104)-net over F₄, using

t-expansion [i] based on digital (73, 259, 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]

(96, 96+163, 144)-Net over F₄ — Digital

Digital (96, 259, 144)-net over F₄, using

t-expansion [i] based on digital (91, 259, 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]

(96, 96+163, 788)-Net in Base 4 — Upper bound on s

There is no (96, 259, 789)-net in base 4, because

1 times m-reduction [i] would yield (96, 258, 789)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 216154 958188 382307 013444 629302 357584 863345 670633 997346 100162 046978 509785 766806 135431 120443 488020 289357 212554 216702 011082 489514 322238 811941 227108 405015 376960 > 4²⁵⁸ [i]