MinT - Best Known (200−49, 200, s)-Nets in Base 4

Best Known (200−49, 200, s)-Nets in Base 4

(200−49, 200, 1032)-Net over F₄ — Constructive and digital

Digital (151, 200, 1032)-net over F₄, using

trace code for nets [i] based on digital (1, 50, 258)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(200−49, 200, 2039)-Net over F₄ — Digital

Digital (151, 200, 2039)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(200−49, 200, 320845)-Net in Base 4 — Upper bound on s

There is no (151, 200, 320846)-net in base 4, because

1 times m-reduction [i] would yield (151, 199, 320846)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 645590 294805 294285 221014 127126 662394 048403 384405 976933 464529 786966 547233 629028 872579 747399 233903 774312 531463 270687 926236 > 4¹⁹⁹ [i]