MinT - Best Known (40, 40+103, s)-Nets in Base 5

Best Known (40, 40+103, s)-Nets in Base 5

(40, 40+103, 78)-Net over F₅ — Constructive and digital

Digital (40, 143, 78)-net over F₅, using

t-expansion [i] based on digital (38, 143, 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]

(40, 40+103, 401)-Net in Base 5 — Upper bound on s

There is no (40, 143, 402)-net in base 5, because

1 times m-reduction [i] would yield (40, 142, 402)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1828 179893 481880 220825 966130 972130 631257 258236 128789 541943 207870 895026 988913 842112 802805 228002 889705 > 5¹⁴² [i]