MinT - Best Known (102−52, 102, s)-Nets in Base 5

Best Known (102−52, 102, s)-Nets in Base 5

(102−52, 102, 82)-Net over F₅ — Constructive and digital

Digital (50, 102, 82)-net over F₅, using

t-expansion [i] based on digital (48, 102, 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]

(102−52, 102, 99)-Net over F₅ — Digital

Digital (50, 102, 99)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(102−52, 102, 1437)-Net in Base 5 — Upper bound on s

There is no (50, 102, 1438)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 198245 623018 983344 039232 676304 739680 506812 399471 635106 972800 860159 617409 > 5¹⁰² [i]