MinT - Best Known (230−57, 230, s)-Nets in Base 4

Best Known (230−57, 230, s)-Nets in Base 4

(230−57, 230, 1028)-Net over F₄ — Constructive and digital

Digital (173, 230, 1028)-net over F₄, using

4² times duplication [i] based on digital (171, 228, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 57, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
      - the rational function field F₂₅₆(x) [i]
    - Niederreiter sequence [i]

(230−57, 230, 2177)-Net over F₄ — Digital

Digital (173, 230, 2177)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(230−57, 230, 316113)-Net in Base 4 — Upper bound on s

There is no (173, 230, 316114)-net in base 4, because

1 times m-reduction [i] would yield (173, 229, 316114)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 744315 478603 254797 045830 202452 146277 098850 077170 353066 654564 699025 946582 140265 751704 446894 946353 724692 113505 235781 730385 025451 311766 053072 > 4²²⁹ [i]