MinT - Best Known (191−87, 191, s)-Nets in Base 4

Best Known (191−87, 191, s)-Nets in Base 4

(191−87, 191, 130)-Net over F₄ — Constructive and digital

Digital (104, 191, 130)-net over F₄, using

5 times m-reduction [i] based on digital (104, 196, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 98, 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]

(191−87, 191, 185)-Net over F₄ — Digital

Digital (104, 191, 185)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(191−87, 191, 2538)-Net in Base 4 — Upper bound on s

There is no (104, 191, 2539)-net in base 4, because

1 times m-reduction [i] would yield (104, 190, 2539)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 467826 781079 390498 597542 565572 825249 333546 059506 306417 697432 015149 130052 579082 134221 800989 627127 991287 803987 855460 > 4¹⁹⁰ [i]