MinT - Best Known (126, 126+57, s)-Nets in Base 4

Best Known (126, 126+57, s)-Nets in Base 4

(126, 126+57, 312)-Net over F₄ — Constructive and digital

Digital (126, 183, 312)-net over F₄, using

t-expansion [i] based on 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]

(126, 126+57, 661)-Net over F₄ — Digital

Digital (126, 183, 661)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(126, 126+57, 30828)-Net in Base 4 — Upper bound on s

There is no (126, 183, 30829)-net in base 4, because

1 times m-reduction [i] would yield (126, 182, 30829)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 37 594048 002030 242324 181090 536781 999749 004649 547471 038128 521630 825007 804262 346978 584260 372441 712221 364957 315246 > 4¹⁸² [i]