MinT - Best Known (182, 230, s)-Nets in Base 4

Best Known (182, 230, s)-Nets in Base 4

(182, 230, 1539)-Net over F₄ — Constructive and digital

Digital (182, 230, 1539)-net over F₄, using

1 times m-reduction [i] based on digital (182, 231, 1539)-net over F₄, using
- trace code for nets [i] based on digital (28, 77, 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]

(182, 230, 5434)-Net over F₄ — Digital

Digital (182, 230, 5434)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(182, 230, 1922997)-Net in Base 4 — Upper bound on s

There is no (182, 230, 1922998)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 977159 604830 599856 793048 677464 233492 275493 702510 123377 396989 444956 434804 650945 489855 836489 426030 872186 601600 920224 879066 252823 363472 852116 > 4²³⁰ [i]