MinT - Best Known (157−61, 157, s)-Nets in Base 4

Best Known (157−61, 157, s)-Nets in Base 4

(157−61, 157, 130)-Net over F₄ — Constructive and digital

Digital (96, 157, 130)-net over F₄, using

23 times m-reduction [i] based on digital (96, 180, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 90, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(157−61, 157, 262)-Net over F₄ — Digital

Digital (96, 157, 262)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(157−61, 157, 5400)-Net in Base 4 — Upper bound on s

There is no (96, 157, 5401)-net in base 4, because

1 times m-reduction [i] would yield (96, 156, 5401)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8376 617648 242630 284725 835168 163534 857339 282958 005694 932928 699736 109542 812844 126340 014415 092608 > 4¹⁵⁶ [i]