MinT - Best Known (147−67, 147, s)-Nets in Base 4

Best Known (147−67, 147, s)-Nets in Base 4

(147−67, 147, 130)-Net over F₄ — Constructive and digital

Digital (80, 147, 130)-net over F₄, using

1 times m-reduction [i] based on digital (80, 148, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 74, 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]

(147−67, 147, 148)-Net over F₄ — Digital

Digital (80, 147, 148)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(147−67, 147, 1995)-Net in Base 4 — Upper bound on s

There is no (80, 147, 1996)-net in base 4, because

1 times m-reduction [i] would yield (80, 146, 1996)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8002 139579 219288 335423 345401 135048 572987 058240 717559 427277 257772 686896 183609 855239 617674 > 4¹⁴⁶ [i]