MinT - Best Known (172−79, 172, s)-Nets in Base 8

Best Known (172−79, 172, s)-Nets in Base 8

(172−79, 172, 354)-Net over F₈ — Constructive and digital

Digital (93, 172, 354)-net over F₈, using

trace code for nets [i] based on digital (7, 86, 177)-net over F₆₄, using
- net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]

(172−79, 172, 391)-Net over F₈ — Digital

Digital (93, 172, 391)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(172−79, 172, 20021)-Net in Base 8 — Upper bound on s

There is no (93, 172, 20022)-net in base 8, because

1 times m-reduction [i] would yield (93, 171, 20022)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 26840 762244 716996 435859 649025 143628 699733 200354 577829 244218 639978 553746 012997 342517 130226 818211 219698 324986 617034 131827 966510 409635 673982 437923 214379 292536 > 8¹⁷¹ [i]