MinT - Best Known (76, 76+66, s)-Nets in Base 9

Best Known (76, 76+66, s)-Nets in Base 9

(76, 76+66, 320)-Net over F₉ — Constructive and digital

Digital (76, 142, 320)-net over F₉, using

trace code for nets [i] based on digital (5, 71, 160)-net over F₈₁, using
- net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
    - a function field by SÃ©mirat [i]

(76, 76+66, 362)-Net over F₉ — Digital

Digital (76, 142, 362)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(76, 76+66, 20988)-Net in Base 9 — Upper bound on s

There is no (76, 142, 20989)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3182 312675 582273 036571 325479 962553 797554 762677 990360 670621 546510 920351 334375 471770 691640 733704 420787 499079 793964 499065 353348 253436 311785 > 9¹⁴² [i]