MinT - Best Known (132, 250, s)-Nets in Base 4

Best Known (132, 250, s)-Nets in Base 4

(132, 250, 130)-Net over F₄ — Constructive and digital

Digital (132, 250, 130)-net over F₄, using

t-expansion [i] based on digital (105, 250, 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, 250, 210)-Net over F₄ — Digital

Digital (132, 250, 210)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(132, 250, 2657)-Net in Base 4 — Upper bound on s

There is no (132, 250, 2658)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 300998 167597 864355 171404 744406 093961 562832 233598 716773 071291 302576 825588 393394 341547 426220 013023 188900 730471 316094 646568 559941 510253 560818 528991 946080 > 4²⁵⁰ [i]