MinT - Best Known (91, 91+148, s)-Nets in Base 4

Best Known (91, 91+148, s)-Nets in Base 4

(91, 91+148, 104)-Net over F₄ — Constructive and digital

Digital (91, 239, 104)-net over F₄, using

t-expansion [i] based on digital (73, 239, 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]

(91, 91+148, 144)-Net over F₄ — Digital

Digital (91, 239, 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]

(91, 91+148, 772)-Net in Base 4 — Upper bound on s

There is no (91, 239, 773)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 787864 578370 632078 116691 134402 485336 547910 127126 351316 443893 703780 423106 942905 417023 045422 528990 016940 197363 032595 388852 558761 844670 947271 455936 > 4²³⁹ [i]