MinT - Best Known (43, 172, s)-Nets in Base 8

Best Known (43, 172, s)-Nets in Base 8

(43, 172, 98)-Net over F₈ — Constructive and digital

Digital (43, 172, 98)-net over F₈, using

t-expansion [i] based on digital (37, 172, 98)-net over F₈, using
- net from sequence [i] based on digital (37, 97)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
    - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(43, 172, 129)-Net over F₈ — Digital

Digital (43, 172, 129)-net over F₈, using

t-expansion [i] based on digital (38, 172, 129)-net over F₈, using
- net from sequence [i] based on digital (38, 128)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 38 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(43, 172, 872)-Net in Base 8 — Upper bound on s

There is no (43, 172, 873)-net in base 8, because

1 times m-reduction [i] would yield (43, 171, 873)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 28589 235194 589249 297007 424967 047237 715630 848846 006716 850399 368393 259590 417264 019468 289793 482567 025379 459408 217506 013899 388298 060192 440816 405357 996252 529379 > 8¹⁷¹ [i]