MinT - Best Known (170−57, 170, s)-Nets in Base 8

Best Known (170−57, 170, s)-Nets in Base 8

(170−57, 170, 1026)-Net over F₈ — Constructive and digital

Digital (113, 170, 1026)-net over F₈, using

trace code for nets [i] based on digital (28, 85, 513)-net over F₆₄, using
- net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
    - the Hermitian function field over F₆₄ [i]

(170−57, 170, 1738)-Net over F₈ — Digital

Digital (113, 170, 1738)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(170−57, 170, 455704)-Net in Base 8 — Upper bound on s

There is no (113, 170, 455705)-net in base 8, because

1 times m-reduction [i] would yield (113, 169, 455705)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 419 003340 291916 353486 255722 291504 543712 900846 595751 994526 108899 278617 346602 624831 923836 758985 174294 962671 683643 084141 064093 841446 077680 299505 352768 186624 > 8¹⁶⁹ [i]