MinT - Best Known (150−104, 150, s)-Nets in Base 5

Best Known (150−104, 150, s)-Nets in Base 5

(150−104, 150, 78)-Net over F₅ — Constructive and digital

Digital (46, 150, 78)-net over F₅, using

t-expansion [i] based on digital (38, 150, 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]

(150−104, 150, 88)-Net over F₅ — Digital

Digital (46, 150, 88)-net over F₅, using

t-expansion [i] based on digital (45, 150, 88)-net over F₅, using
- net from sequence [i] based on digital (45, 87)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 45 and N(F) ≥ 88, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(150−104, 150, 487)-Net in Base 5 — Upper bound on s

There is no (46, 150, 488)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 744 118210 878488 933855 543047 944110 009995 950854 704687 654951 747468 549505 086836 849443 008915 157044 631133 931521 > 5¹⁵⁰ [i]