MinT - Best Known (66, 66+49, s)-Nets in Base 4

Best Known (66, 66+49, s)-Nets in Base 4

(66, 66+49, 130)-Net over F₄ — Constructive and digital

Digital (66, 115, 130)-net over F₄, using

5 times m-reduction [i] based on digital (66, 120, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 60, 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]

(66, 66+49, 149)-Net over F₄ — Digital

Digital (66, 115, 149)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+49, 2346)-Net in Base 4 — Upper bound on s

There is no (66, 115, 2347)-net in base 4, because

1 times m-reduction [i] would yield (66, 114, 2347)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 433 001022 753643 070134 669723 391687 865197 357768 595822 082298 171705 675434 > 4¹¹⁴ [i]