MinT - Best Known (170−79, 170, s)-Nets in Base 4

Best Known (170−79, 170, s)-Nets in Base 4

(170−79, 170, 130)-Net over F₄ — Constructive and digital

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]

(170−79, 170, 157)-Net over F₄ — Digital

Digital (91, 170, 157)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(170−79, 170, 2053)-Net in Base 4 — Upper bound on s

There is no (91, 170, 2054)-net in base 4, because

1 times m-reduction [i] would yield (91, 169, 2054)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 562193 136313 338227 739459 484829 587736 824511 459704 769843 959605 880776 954551 442403 757722 514018 676094 167040 > 4¹⁶⁹ [i]