MinT - Best Known (162−64, 162, s)-Nets in Base 4

Best Known (162−64, 162, s)-Nets in Base 4

(162−64, 162, 130)-Net over F₄ — Constructive and digital

Digital (98, 162, 130)-net over F₄, using

22 times m-reduction [i] based on digital (98, 184, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 92, 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]

(162−64, 162, 254)-Net over F₄ — Digital

Digital (98, 162, 254)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(162−64, 162, 4734)-Net in Base 4 — Upper bound on s

There is no (98, 162, 4735)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 34 227556 316484 730372 699498 983791 835714 903447 207633 322978 139185 361159 050442 160169 844564 846323 086277 > 4¹⁶² [i]