MinT - Best Known (93, 93+57, s)-Nets in Base 5

Best Known (93, 93+57, s)-Nets in Base 5

(93, 93+57, 252)-Net over F₅ — Constructive and digital

Digital (93, 150, 252)-net over F₅, using

t-expansion [i] based on digital (85, 150, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 75, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
      - the Hermitian function field over F₂₅ [i]

(93, 93+57, 387)-Net over F₅ — Digital

Digital (93, 150, 387)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(93, 93+57, 14786)-Net in Base 5 — Upper bound on s

There is no (93, 150, 14787)-net in base 5, because

1 times m-reduction [i] would yield (93, 149, 14787)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 140 287616 570782 284594 351737 084712 235957 366045 649155 399291 725392 118909 897352 551824 776988 058541 786203 048465 > 5¹⁴⁹ [i]