MinT - Best Known (132, 259, s)-Nets in Base 4

Best Known (132, 259, s)-Nets in Base 4

(132, 259, 130)-Net over F₄ — Constructive and digital

Digital (132, 259, 130)-net over F₄, using

t-expansion [i] based on 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]

(132, 259, 192)-Net over F₄ — Digital

Digital (132, 259, 192)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(132, 259, 2315)-Net in Base 4 — Upper bound on s

There is no (132, 259, 2316)-net in base 4, because

1 times m-reduction [i] would yield (132, 258, 2316)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 220021 497046 232208 092147 567160 584223 040972 678560 484286 571100 417605 869068 156922 117623 376075 434255 194560 992895 750210 175445 106510 965481 043545 132671 361289 868480 > 4²⁵⁸ [i]