MinT - Best Known (101−49, 101, s)-Nets in Base 5

Best Known (101−49, 101, s)-Nets in Base 5

(101−49, 101, 82)-Net over F₅ — Constructive and digital

Digital (52, 101, 82)-net over F₅, using

t-expansion [i] based on digital (48, 101, 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]

(101−49, 101, 116)-Net over F₅ — Digital

Digital (52, 101, 116)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(101−49, 101, 1985)-Net in Base 5 — Upper bound on s

There is no (52, 101, 1986)-net in base 5, because

1 times m-reduction [i] would yield (52, 100, 1986)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 7932 196748 158274 929836 918764 804896 566818 511566 701984 090070 439182 788225 > 5¹⁰⁰ [i]