MinT - Best Known (144−34, 144, s)-Nets in Base 4

Best Known (144−34, 144, s)-Nets in Base 4

(144−34, 144, 1036)-Net over F₄ — Constructive and digital

Digital (110, 144, 1036)-net over F₄, using

trace code for nets [i] based on digital (2, 36, 259)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(144−34, 144, 1876)-Net over F₄ — Digital

Digital (110, 144, 1876)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(144−34, 144, 301027)-Net in Base 4 — Upper bound on s

There is no (110, 144, 301028)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 497 330591 785147 418592 034287 563185 158438 665600 496072 242540 334466 700279 126055 796673 964562 > 4¹⁴⁴ [i]