MinT - Best Known (50, 50+48, s)-Nets in Base 5

Best Known (50, 50+48, s)-Nets in Base 5

(50, 50+48, 82)-Net over F₅ — Constructive and digital

Digital (50, 98, 82)-net over F₅, using

t-expansion [i] based on digital (48, 98, 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]

(50, 50+48, 110)-Net over F₅ — Digital

Digital (50, 98, 110)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(50, 50+48, 1734)-Net in Base 5 — Upper bound on s

There is no (50, 98, 1735)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 319 267375 938950 176757 719277 218366 979396 226411 355115 868786 197089 927585 > 5⁹⁸ [i]