MinT - Best Known (91, 91+153, s)-Nets in Base 4

Best Known (91, 91+153, s)-Nets in Base 4

(91, 91+153, 104)-Net over F₄ — Constructive and digital

Digital (91, 244, 104)-net over F₄, using

t-expansion [i] based on digital (73, 244, 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+153, 144)-Net over F₄ — Digital

Digital (91, 244, 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+153, 755)-Net in Base 4 — Upper bound on s

There is no (91, 244, 756)-net in base 4, because

1 times m-reduction [i] would yield (91, 243, 756)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 207 557754 479869 896256 220913 923519 224227 669584 402077 711452 106285 807350 951425 182065 886448 072376 868855 859331 803692 057551 657969 250910 736241 815363 497116 > 4²⁴³ [i]