MinT - Best Known (125, 125+58, s)-Nets in Base 4

Best Known (125, 125+58, s)-Nets in Base 4

(125, 125+58, 312)-Net over F₄ — Constructive and digital

Digital (125, 183, 312)-net over F₄, using

trace code for nets [i] based on digital (3, 61, 104)-net over F₆₄, using
- net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
    - a function field by SÃ©mirat [i]

(125, 125+58, 617)-Net over F₄ — Digital

Digital (125, 183, 617)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(125, 125+58, 24478)-Net in Base 4 — Upper bound on s

There is no (125, 183, 24479)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 150 369673 150801 503240 136196 383406 673211 219199 102283 693928 341634 907093 274685 589225 709622 841724 802527 172718 413414 > 4¹⁸³ [i]