MinT - Best Known (66, 66+41, s)-Nets in Base 4

Best Known (66, 66+41, s)-Nets in Base 4

(66, 66+41, 130)-Net over F₄ — Constructive and digital

Digital (66, 107, 130)-net over F₄, using

13 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+41, 200)-Net over F₄ — Digital

Digital (66, 107, 200)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+41, 4280)-Net in Base 4 — Upper bound on s

There is no (66, 107, 4281)-net in base 4, because

1 times m-reduction [i] would yield (66, 106, 4281)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6605 367612 332714 483607 408602 697315 391726 696414 979052 383962 600534 > 4¹⁰⁶ [i]