MinT - Best Known (162−71, 162, s)-Nets in Base 4

Best Known (162−71, 162, s)-Nets in Base 4

(162−71, 162, 130)-Net over F₄ — Constructive and digital

Digital (91, 162, 130)-net over F₄, using

8 times m-reduction [i] based on digital (91, 170, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 85, 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]

(162−71, 162, 182)-Net over F₄ — Digital

Digital (91, 162, 182)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(162−71, 162, 2698)-Net in Base 4 — Upper bound on s

There is no (91, 162, 2699)-net in base 4, because

1 times m-reduction [i] would yield (91, 161, 2699)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8 650988 662522 984742 430178 141674 356095 738493 134533 454611 105278 042580 539435 228543 031099 632491 736560 > 4¹⁶¹ [i]