MinT - Best Known (157−63, 157, s)-Nets in Base 4

Best Known (157−63, 157, s)-Nets in Base 4

(157−63, 157, 130)-Net over F₄ — Constructive and digital

Digital (94, 157, 130)-net over F₄, using

19 times m-reduction [i] based on digital (94, 176, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 88, 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]

(157−63, 157, 235)-Net over F₄ — Digital

Digital (94, 157, 235)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(157−63, 157, 4407)-Net in Base 4 — Upper bound on s

There is no (94, 157, 4408)-net in base 4, because

1 times m-reduction [i] would yield (94, 156, 4408)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8398 672472 636679 751093 847570 121390 246004 583087 653418 857907 558258 506743 390719 098876 544768 762860 > 4¹⁵⁶ [i]