MinT - Best Known (234−49, 234, s)-Nets in Base 4

Best Known (234−49, 234, s)-Nets in Base 4

(234−49, 234, 1539)-Net over F₄ — Constructive and digital

Digital (185, 234, 1539)-net over F₄, using

t-expansion [i] based on digital (184, 234, 1539)-net over F₄, using
- trace code for nets [i] based on digital (28, 78, 513)-net over F₆₄, using
  - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
      - the Hermitian function field over F₆₄ [i]

(234−49, 234, 5403)-Net over F₄ — Digital

Digital (185, 234, 5403)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(234−49, 234, 2286845)-Net in Base 4 — Upper bound on s

There is no (185, 234, 2286846)-net in base 4, because

1 times m-reduction [i] would yield (185, 233, 2286846)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 190 537028 427754 366434 157836 530107 234065 964370 774904 191692 971179 978786 586441 722394 569171 877654 589030 229761 254149 883109 915702 427673 951866 376661 > 4²³³ [i]