MinT - Best Known (126, 126+54, s)-Nets in Base 4

Best Known (126, 126+54, s)-Nets in Base 4

(126, 126+54, 384)-Net over F₄ — Constructive and digital

Digital (126, 180, 384)-net over F₄, using

t-expansion [i] based on digital (125, 180, 384)-net over F₄, using
- trace code for nets [i] based on digital (5, 60, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(126, 126+54, 760)-Net over F₄ — Digital

Digital (126, 180, 760)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(126, 126+54, 37563)-Net in Base 4 — Upper bound on s

There is no (126, 180, 37564)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 349603 036327 972918 966495 114428 498950 071583 980607 909933 391436 103836 170127 436234 458849 256729 651053 588466 172125 > 4¹⁸⁰ [i]