MinT - Best Known (167−108, 167, s)-Nets in Base 8

Best Known (167−108, 167, s)-Nets in Base 8

(167−108, 167, 98)-Net over F₈ — Constructive and digital

Digital (59, 167, 98)-net over F₈, using

t-expansion [i] based on digital (37, 167, 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]

(167−108, 167, 144)-Net over F₈ — Digital

Digital (59, 167, 144)-net over F₈, using

t-expansion [i] based on digital (45, 167, 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]

(167−108, 167, 1825)-Net in Base 8 — Upper bound on s

There is no (59, 167, 1826)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6 698669 773815 190530 179274 626033 806692 971518 684972 278627 237293 967832 938158 469847 333668 905350 428596 646371 197841 293282 319423 620700 749307 562190 234306 524032 > 8¹⁶⁷ [i]