MinT - Best Known (64, 137, s)-Nets in Base 5

Best Known (64, 137, s)-Nets in Base 5

(64, 137, 82)-Net over F₅ — Constructive and digital

Digital (64, 137, 82)-net over F₅, using

t-expansion [i] based on digital (48, 137, 82)-net over F₅, using
- net from sequence [i] based on digital (48, 81)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 48 and N(F) ≥ 82, using
    - an explicitly constructive algebraic function field [i]

(64, 137, 120)-Net over F₅ — Digital

Digital (64, 137, 120)-net over F₅, using

t-expansion [i] based on digital (61, 137, 120)-net over F₅, using
- net from sequence [i] based on digital (61, 119)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 61 and N(F) ≥ 120, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(64, 137, 1534)-Net in Base 5 — Upper bound on s

There is no (64, 137, 1535)-net in base 5, because

1 times m-reduction [i] would yield (64, 136, 1535)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 117365 658057 388128 361766 626327 849679 187875 422217 596939 872894 279570 761932 689108 917741 321626 042225 > 5¹³⁶ [i]