MinT - Best Known (91, 91+159, s)-Nets in Base 4

Best Known (91, 91+159, s)-Nets in Base 4

(91, 91+159, 104)-Net over F₄ — Constructive and digital

Digital (91, 250, 104)-net over F₄, using

t-expansion [i] based on digital (73, 250, 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+159, 144)-Net over F₄ — Digital

Digital (91, 250, 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+159, 732)-Net in Base 4 — Upper bound on s

There is no (91, 250, 733)-net in base 4, because

1 times m-reduction [i] would yield (91, 249, 733)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 849469 477713 435304 826527 491397 121103 094386 752141 276131 218761 867569 475685 365860 619461 266566 652900 185203 429196 998165 471541 334892 217416 372092 022799 817616 > 4²⁴⁹ [i]