MinT - Best Known (118−79, 118, s)-Nets in Base 5

Best Known (118−79, 118, s)-Nets in Base 5

(118−79, 118, 78)-Net over F₅ — Constructive and digital

Digital (39, 118, 78)-net over F₅, using

t-expansion [i] based on digital (38, 118, 78)-net over F₅, using
- net from sequence [i] based on digital (38, 77)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 38 and N(F) ≥ 78, using
    - an explicitly constructive algebraic function field [i]

(118−79, 118, 452)-Net in Base 5 — Upper bound on s

There is no (39, 118, 453)-net in base 5, because

1 times m-reduction [i] would yield (39, 117, 453)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 6023 616533 270897 222991 254592 594730 311632 394734 149320 171909 306173 257662 501916 163325 > 5¹¹⁷ [i]