MinT - Best Known (202−99, 202, s)-Nets in Base 3

Best Known (202−99, 202, s)-Nets in Base 3

(202−99, 202, 74)-Net over F₃ — Constructive and digital

Digital (103, 202, 74)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (27, 76, 37)-net over F₃, using
  - net from sequence [i] based on digital (27, 36)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₃ with g(F)Â =Â 26, N(F)Â =Â 36, and 1 place with degree 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
2. digital (27, 126, 37)-net over F₃, using
  - net from sequence [i] based on digital (27, 36)-sequence over F₃ (see above)

(202−99, 202, 107)-Net over F₃ — Digital

Digital (103, 202, 107)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(202−99, 202, 818)-Net in Base 3 — Upper bound on s

There is no (103, 202, 819)-net in base 3, because

1 times m-reduction [i] would yield (103, 201, 819)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 821494 767645 156820 046508 856736 900602 820270 633961 816027 694380 515318 727489 713823 729666 790389 236103 > 3²⁰¹ [i]