MinT - Best Known (80, 80+65, s)-Nets in Base 4

Best Known (80, 80+65, s)-Nets in Base 4

(80, 80+65, 130)-Net over F₄ — Constructive and digital

Digital (80, 145, 130)-net over F₄, using

3 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]

(80, 80+65, 154)-Net over F₄ — Digital

Digital (80, 145, 154)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(80, 80+65, 2156)-Net in Base 4 — Upper bound on s

There is no (80, 145, 2157)-net in base 4, because

1 times m-reduction [i] would yield (80, 144, 2157)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 498 570602 360130 924946 682419 678227 793346 107191 481311 571625 838912 253344 505282 374944 869915 > 4¹⁴⁴ [i]