MinT - Best Known (166−67, 166, s)-Nets in Base 4

Best Known (166−67, 166, s)-Nets in Base 4

(166−67, 166, 130)-Net over F₄ — Constructive and digital

Digital (99, 166, 130)-net over F₄, using

20 times m-reduction [i] based on digital (99, 186, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 93, 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]

(166−67, 166, 241)-Net over F₄ — Digital

Digital (99, 166, 241)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(166−67, 166, 4466)-Net in Base 4 — Upper bound on s

There is no (99, 166, 4467)-net in base 4, because

1 times m-reduction [i] would yield (99, 165, 4467)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2202 971605 802371 004813 645706 929367 464962 660130 035558 202926 818455 909089 165247 176173 986970 368437 515322 > 4¹⁶⁵ [i]