MinT - Best Known (131, 131+129, s)-Nets in Base 4

Best Known (131, 131+129, s)-Nets in Base 4

(131, 131+129, 130)-Net over F₄ — Constructive and digital

Digital (131, 260, 130)-net over F₄, using

t-expansion [i] based on digital (105, 260, 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]

(131, 131+129, 186)-Net over F₄ — Digital

Digital (131, 260, 186)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(131, 131+129, 2194)-Net in Base 4 — Upper bound on s

There is no (131, 260, 2195)-net in base 4, because

1 times m-reduction [i] would yield (131, 259, 2195)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 869863 055556 899462 139095 463961 084255 868431 596337 326407 755766 964955 406214 503196 116364 204065 576846 368453 960156 197079 480236 250737 649995 826691 409244 111932 755470 > 4²⁵⁹ [i]