MinT - Best Known (60, 60+37, s)-Nets in Base 5

Best Known (60, 60+37, s)-Nets in Base 5

(60, 60+37, 252)-Net over F₅ — Constructive and digital

Digital (60, 97, 252)-net over F₅, using

3 times m-reduction [i] based on digital (60, 100, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 50, 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]

(60, 60+37, 268)-Net over F₅ — Digital

Digital (60, 97, 268)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(60, 60+37, 10077)-Net in Base 5 — Upper bound on s

There is no (60, 97, 10078)-net in base 5, because

1 times m-reduction [i] would yield (60, 96, 10078)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 12 634260 697096 328694 143574 837422 010368 098326 677735 401539 677478 753025 > 5⁹⁶ [i]