MinT - Best Known (105, 236, s)-Nets in Base 4

Best Known (105, 236, s)-Nets in Base 4

(105, 236, 130)-Net over F₄ — Constructive and digital

Digital (105, 236, 130)-net over F₄, using

net from sequence [i] based on digital (105, 129)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
  - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(105, 236, 144)-Net over F₄ — Digital

Digital (105, 236, 144)-net over F₄, using

t-expansion [i] based on digital (91, 236, 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]

(105, 236, 1201)-Net in Base 4 — Upper bound on s

There is no (105, 236, 1202)-net in base 4, because

1 times m-reduction [i] would yield (105, 235, 1202)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3192 320122 229047 926245 594340 520978 297459 778514 588300 343951 107847 333230 571773 904094 416762 394245 068074 187609 192905 987513 826726 598270 882602 361030 > 4²³⁵ [i]