MinT - Best Known (108, 108+82, s)-Nets in Base 4

Best Known (108, 108+82, s)-Nets in Base 4

(108, 108+82, 130)-Net over F₄ — Constructive and digital

Digital (108, 190, 130)-net over F₄, using

t-expansion [i] based on digital (105, 190, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(108, 108+82, 219)-Net over F₄ — Digital

Digital (108, 190, 219)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(108, 108+82, 3284)-Net in Base 4 — Upper bound on s

There is no (108, 190, 3285)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 490880 338880 237070 454902 820257 198692 442114 026261 709154 482986 807428 922047 831059 457822 902975 925280 609164 204781 368736 > 4¹⁹⁰ [i]