MinT - Best Known (233−47, 233, s)-Nets in Base 4

Best Known (233−47, 233, s)-Nets in Base 4

(233−47, 233, 1539)-Net over F₄ — Constructive and digital

Digital (186, 233, 1539)-net over F₄, using

4 times m-reduction [i] based on digital (186, 237, 1539)-net over F₄, using
- trace code for nets [i] based on digital (28, 79, 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]

(233−47, 233, 6747)-Net over F₄ — Digital

Digital (186, 233, 6747)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(233−47, 233, 3717798)-Net in Base 4 — Upper bound on s

There is no (186, 233, 3717799)-net in base 4, because

1 times m-reduction [i] would yield (186, 232, 3717799)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 47 634370 092157 953489 884610 765654 361592 594317 261819 908446 013130 395470 701380 204764 183943 945624 304073 787844 871012 013344 950751 792518 559416 743112 > 4²³² [i]