MinT - Best Known (170−71, 170, s)-Nets in Base 4

Best Known (170−71, 170, s)-Nets in Base 4

(170−71, 170, 130)-Net over F₄ — Constructive and digital

Digital (99, 170, 130)-net over F₄, using

16 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]

(170−71, 170, 221)-Net over F₄ — Digital

Digital (99, 170, 221)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(170−71, 170, 3714)-Net in Base 4 — Upper bound on s

There is no (99, 170, 3715)-net in base 4, because

1 times m-reduction [i] would yield (99, 169, 3715)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 562433 999687 795626 463789 524981 610873 376188 496344 120537 380542 597358 524979 404448 962219 603760 058051 261584 > 4¹⁶⁹ [i]