MinT - Best Known (126−78, 126, s)-Nets in Base 8

Best Known (126−78, 126, s)-Nets in Base 8

(126−78, 126, 98)-Net over F₈ — Constructive and digital

Digital (48, 126, 98)-net over F₈, using

t-expansion [i] based on digital (37, 126, 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]

(126−78, 126, 144)-Net over F₈ — Digital

Digital (48, 126, 144)-net over F₈, using

t-expansion [i] based on digital (45, 126, 144)-net over F₈, using
- net from sequence [i] based on digital (45, 143)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(126−78, 126, 1795)-Net in Base 8 — Upper bound on s

There is no (48, 126, 1796)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 625753 156832 388308 487596 158321 391819 626641 818007 583182 701245 705905 105344 191615 388135 340999 636302 883303 697171 817280 > 8¹²⁶ [i]