MinT - Best Known (259−154, 259, s)-Nets in Base 4

Best Known (259−154, 259, s)-Nets in Base 4

(259−154, 259, 130)-Net over F₄ — Constructive and digital

Digital (105, 259, 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]

(259−154, 259, 144)-Net over F₄ — Digital

Digital (105, 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]

(259−154, 259, 979)-Net in Base 4 — Upper bound on s

There is no (105, 259, 980)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 911138 750922 136528 213242 647222 982105 649421 323452 875947 494837 047438 529060 455128 211082 701477 894242 058898 826246 900747 831901 828494 007910 000849 708731 790153 665116 > 4²⁵⁹ [i]