MinT - Best Known (208−47, 208, s)-Nets in Base 4

Best Known (208−47, 208, s)-Nets in Base 4

(208−47, 208, 1048)-Net over F₄ — Constructive and digital

Digital (161, 208, 1048)-net over F₄, using

trace code for nets [i] based on digital (5, 52, 262)-net over F₂₅₆, using
- net from sequence [i] based on digital (5, 261)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(208−47, 208, 3188)-Net over F₄ — Digital

Digital (161, 208, 3188)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(208−47, 208, 823882)-Net in Base 4 — Upper bound on s

There is no (161, 208, 823883)-net in base 4, because

1 times m-reduction [i] would yield (161, 207, 823883)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 42308 555716 399240 250501 630778 808497 810662 996410 174208 556368 387577 970821 854830 332276 930639 525961 537092 544299 027972 794279 495680 > 4²⁰⁷ [i]